B. Venkatesh
Mutual funds portfolios are typically diversified. Self-directed portfolios, on the other hand, are mostly concentrated. Both strive to beat the market. Or in other words, generate alpha. The question is: Which portfolio is more optimal for active management?
This article explains the role of diversified and concentrated portfolios in alpha generation. It then shows why the choice of portfolio construction is dependent on the alpha source and investment style.
Diversified alpha
Alpha is primarily generated by security selection. That is, a portfolio manager will go overweight on a security that she believes will outperform the index of which it is a constituent. There is a fundamental law of active management. It states that the Information Ratio is equal to product of Information Coefficient and square root of breadth.
Information Ratio, to recap, is the residual or excess returns divided by the volatility of residual return - the numerator captures the excess return and the denominator, the risk assumed to generate such returns.
Suffice it to know that the excess (alpha) return is a function of the manager`s skills (Information Coefficient) and her independent investment bets per year (Breadth). According to this argument, a portfolio manager can increase the portfolio`s Information Ratio by spreading her spreads across more stocks and/or increasing her skill.
A portfolio manager`s skill is captured by how close (correlation) her forecast of residual returns is to realized returns. As this variable is not so easy to improve, the manager is left to increase her independent bets to improve the Information Ratio. This is the reason professional managers prefer diversified portfolio.
It then follows that an investor adopting traditional investment style using security selection as the alpha source should strive to have a meaningful collection of stocks to improve Information Ratio.
Suppose we define the portfolio`s risk as the total of market risk and residual risk. We can then state that market returns (beta) is the compensation for market risk and alpha, the compensation for residual risk.
Now, a portfolio`s market risk can be captured by its R-squared, which measures the completeness of the diversification relative to the market or benchmark. A portfolio with R-squared of one will have no residual risk. Research has shown that nearly a third of a typical stock`s behavior can be explained by market factors. In other words, for a typical stock, the R-squared is 0.30. But when large number of such stocks is gathered into a portfolio, the portfolio`s R-squared typically exceeds 0.90.
It follows from this argument that one way to retain more non-market risk exposure and generate non-market returns (alpha) is to have a concentrated portfolio. Two kinds of investors prefer such concentrated portfolios. Hedge funds that engage in arbitrage trades apply quantitative models to place large leveraged bets on fewer assets. Individuals managing self-directed portfolios apply technical analysis to invest in few assets to time the market.
Mutual funds portfolios are typically diversified. Self-directed portfolios, on the other hand, are mostly concentrated. Both strive to beat the market. Or in other words, generate alpha. The question is: Which portfolio is more optimal for active management?
This article explains the role of diversified and concentrated portfolios in alpha generation. It then shows why the choice of portfolio construction is dependent on the alpha source and investment style.
Diversified alpha
Alpha is primarily generated by security selection. That is, a portfolio manager will go overweight on a security that she believes will outperform the index of which it is a constituent. There is a fundamental law of active management. It states that the Information Ratio is equal to product of Information Coefficient and square root of breadth.
Information Ratio, to recap, is the residual or excess returns divided by the volatility of residual return - the numerator captures the excess return and the denominator, the risk assumed to generate such returns.
Suffice it to know that the excess (alpha) return is a function of the manager`s skills (Information Coefficient) and her independent investment bets per year (Breadth). According to this argument, a portfolio manager can increase the portfolio`s Information Ratio by spreading her spreads across more stocks and/or increasing her skill.
A portfolio manager`s skill is captured by how close (correlation) her forecast of residual returns is to realized returns. As this variable is not so easy to improve, the manager is left to increase her independent bets to improve the Information Ratio. This is the reason professional managers prefer diversified portfolio.
It then follows that an investor adopting traditional investment style using security selection as the alpha source should strive to have a meaningful collection of stocks to improve Information Ratio.
Suppose we define the portfolio`s risk as the total of market risk and residual risk. We can then state that market returns (beta) is the compensation for market risk and alpha, the compensation for residual risk.
Now, a portfolio`s market risk can be captured by its R-squared, which measures the completeness of the diversification relative to the market or benchmark. A portfolio with R-squared of one will have no residual risk. Research has shown that nearly a third of a typical stock`s behavior can be explained by market factors. In other words, for a typical stock, the R-squared is 0.30. But when large number of such stocks is gathered into a portfolio, the portfolio`s R-squared typically exceeds 0.90.
It follows from this argument that one way to retain more non-market risk exposure and generate non-market returns (alpha) is to have a concentrated portfolio. Two kinds of investors prefer such concentrated portfolios. Hedge funds that engage in arbitrage trades apply quantitative models to place large leveraged bets on fewer assets. Individuals managing self-directed portfolios apply technical analysis to invest in few assets to time the market.
Note that the fundamental law of active management essentially scoffs at market timers as such strategy has low Information Ratio. This is because market timers take large bets on fewer stocks and, hence, have lower breadth. The key to succeeding in market timing strategy is to have strict risk management rules to contain losses.
Conclusion
The above discussion shows that both diversified and concentrated portfolios have the potential to generate alpha. It would be optimal for those who follow technical analysis or other trend-following system to construct concentrated portfolios with strict risk management rules to contain losses on wrong bets. Those who follow traditional form of investing (fundamental analysis, for instance) should prefer diversified portfolio with independent alpha bets that do not largely cancel each other. That is, a factor that drives the excess return on one stock should not lead to negative returns on another. Otherwise, diversification can lead to tighter R-squared making the portfolio a closed indexer.
Conclusion
The above discussion shows that both diversified and concentrated portfolios have the potential to generate alpha. It would be optimal for those who follow technical analysis or other trend-following system to construct concentrated portfolios with strict risk management rules to contain losses on wrong bets. Those who follow traditional form of investing (fundamental analysis, for instance) should prefer diversified portfolio with independent alpha bets that do not largely cancel each other. That is, a factor that drives the excess return on one stock should not lead to negative returns on another. Otherwise, diversification can lead to tighter R-squared making the portfolio a closed indexer.
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